Abstract Cells inside tissues and biomaterials receive mechanical cues that affect the cells? morphology and function. These phenotype changes in turn can remodel the extracellular environment. To understand this intricate interaction, it is fundamentally necessary to measure the mechanical properties of both intracellular and extracellular space in situ. However, this measurement is very difficult by the lack of suitable tools. The goal of this project is to develop novel optical tools based on stimulated Brillouin scattering (SBS) for measuring and mapping stiffness with 3D resolution. The first specific aim is to develop a longitudinal-wave SBS microscope system using a pulsed scheme to achieve sub-millisecond data acquisition speed, 1000-fold improved over spontaneous Brillouin microscopy. The second specific aim is to develop a shear-wave SBS microscope system. Using the coherent nature of SBS, this new modality may measure shear modulus in a broad range from 100 Pa to 1 MPa with subcellular resolution. The third specific aim is to combine the two systems with a common sample stage allowing both longitudinal and shear moduli to be measured from each microscopic volume. The combined microscope will provide unprecedented label-free, high-resolution access to the full compliance or stiffness tensors of cells, tissues, and hydrogels. The successful development of SBS microscopy will have a major impact on many areas that require mechanical characterization of biomaterials, cells, organoids, tissue slices, and small living organisms at high spatial resolution.